No. All we can do is to remove the existing VM and create a new VM with that same VHD (Virtual Hard Disk), deploying it to the virtual network.
When we remove an existing VM, the VHD for it remains and is registered as a disk in the portal. So when we create a new one, we can just select that disk under My Disks in the portal to reuse it.
But there is no method to move it into the virtual network once the VM is created.